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\(17.8+51.4=34.4+51.4=4\left(51+34\right)=4.84=336\) \(2.2.3.5.19=\left(2.5\right).\left(3.19\right).2=10.2.57=570.2=1140\) \(54.275+825.15+275=54.275+45.275+275=275\left(54+45+1\right)=100.275=27500\) \(\frac{167.198+98}{198.168-100}=\frac{167.198+98}{198.167+198-100}=\frac{167.198+98}{167.198+98}=1\)
\(\frac{1}{n}-\frac{1}{n+k}=\frac{k}{n\left(n+k\right)}\Rightarrow\frac{1}{1.2}+\frac{1}{2.3}+.....+\frac{1}{2019.2020}=1-\frac{1}{2}+\frac{1}{2}-....-\frac{1}{2020}=1-\frac{1}{2020}=\frac{2019}{2020}\)
a) 17 x 8 + 51 x 4
= 17 x 4 x 2 + 17 x 3 x 4
= 17 x 4 x ( 2 + 3 )
= 14 x 4 x 5
= 14 x 20
= 280
b) 2 x 2 x 3 x 5 x 19
= ( 2 x 5 ) x ( 3 x 19 ) x 2
= 10 x 57 x 2
= 570 x 2
= 1140
c) 54 x 275 + 825 x 15 + 275
= 54 x 275 + 275 x 3 x 15 + 275 x 1
= 54 x 275 + 275 x 45 + 275 x 1
= 275 x ( 54 + 45 + 1 )
= 275 x 100
= 27500
d) 100 - 99 + 98 - 97 + 96 - 95 + 94 - 93 + ... + 4 - 3 + 2
= (100 - 99) + (98 - 97) + (96 - 95) + (94 - 93) + ... + (4 - 3) + 2
= (1 + 1 + ... + 1) + 2
( 49 số 1 )
= 49 + 2
= 51
k) 1,5 + 2,5 + 3,5 + 4,5 + 5,5 + 6,5 + 7,5 + 8,5
= ( 1,5 + 8,5 ) + ( 2,5 + 7,5 ) + ( 3,5 + 6,5 ) + ( 4,5 + 5,5 )
= 10 + 10 + 10 + 10
= 40
1) 120 + 20 : 4 - 22.3
=> 120 + 5 - 12
=> 125-12
=>113
2) ( 120 + 20 ) : 4 - 22 . 3
=> 140 : 4 - 12
=> 35 - 12
=> 23
3) 120 + ( 20 : 4 - 22 ).3
=> 120 + 1 . 3
=> 120 + 3
=> 123
1)120+20:4-2\(^2\) .3=120+5-4.3=120+5-12=113
2)(120+20):4-2\(^2\) .3=140:4-4.3=35-12=23
3)120+(20:4-2\(^2\) ).3=120+(5-4).3=120+1.3=120+3=123
Bài 30 :
a ) Ta có :
( a + b ) ( a - b )
= ( a + b ) . a - ( a + b ) . b
= a . a + ab - ab - b . b
= a2 + ab - ab - b2
= a2 - b2 ( điều phải chứng minh )
b ) M = 1002 - 992 + 982 - 972 + 962 - 952 + ..... + 42 - 32 + 22 - 12
M = 199 + 195 + 191 + ...... + 7 + 3
M = ( 199 + 3 ) x [ ( 199 - 3 ) : 4 + 1 ] : 2
M = 202 x 50 : 2
M = 10100 : 2
M = 5050
30) Ta có : \(\left(a+b\right)\left(a-b\right)\)
\(=\left(a+b\right)a-\left(a+b\right).b\)
\(=a^2+ab-ab-b^2\)
\(=a^2-b^2\left(đpcm\right)\)
\(4^{3x+1}-8.4^2=8.4^2\)
\(\Rightarrow4^{3x}.4=8.4^2+8.4^2=16.4^2\)
\(\Rightarrow4^{3^x}=4.4.4=4^3\)
\(\Rightarrow3x=3\)
\(\Rightarrow x=1\)
\(7^{5x-1}=7^4\)
\(\Rightarrow5x-1=4\)
\(\Rightarrow5x=5\)
\(\Rightarrow x=1\)
\(M=2-2^2+2^3-2^4+...+2^{19}-2^{10}\\ 2.M=2^2-2^3+2^4-2^5+...+2^{20}-2^{21}\\ 2.M+M=2^{21}+2\\ \Rightarrow M=\frac{2^{21}+2}{3}\)
\(P=4^{100}-4^{98}+4^{96}-4^{94}+...+4^4-4^2\\ 4^2.P=4^{102}-4^{100}+4^{98}-4^{96}+...+4^6-4^4\\ 4^2.P+P=4^{102}-4^2\\ \Rightarrow P=\frac{4^{102}-4^2}{17}\)